A Formal Theory for Vortex Rossby Waves and Vortex Evolution

McWilliams, James C.; Graves, Lee Paul; Montgomery, Michael T.

doi:10.1080/0309192031000108698

Cited by 63 publications

(63 citation statements)

References 49 publications

(42 reference statements)

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“…During sub-periods of positive spin-up tendency, the animations suggest a sequence of local cyclonic vorticity generation, followed by a tendency of vortex axisymmetrization and trailing-spiral vorticity bands, which partially encircle the cyclonic mesoscale vorticity region near the RMW. These banded features appear plausibly consistent with convectively coupled sheared vortex Rossby waves that would act to strengthen the mean vortex at radii interior to their excitation radius (Montgomery and Kallenbach, 1997;Montgomery and Enagonio, 1998;Wang, 2002a, b;Chen et al, 2003;McWilliams et al, 2003). We pause now to elucidate further the physical nature of the horizontal and vertical eddies in the 3D3k simulation during the second period of intensification.…”

Section: Discussion Of Eddy Dynamicsmentioning

confidence: 99%

“…This is the "non-acceleration theorem" for inviscid, axisymmetric balance vortex dynamics (cf. McWilliams et al, 2003).…”

Section: Deductions From the Spin-up Functionmentioning

confidence: 99%

“…2 VRWs are analogues of planetary Rossby waves (e.g., Holton, 2004), but propagate on the potential vorticity gradient of the system-scale vortex and are affected by the corresponding differential rotation in the radial and vertical direction (Shapiro and Montgomery, 1993;Guinn and Schubert, 1993;Montgomery and Kallenbach, 1997;Schubert et al, 1999;Möller and Montgomery, 2000;McWilliams et al, 2003).…”

Section: Role Of Vortical Deep Convection In Tropical Cyclonesmentioning

confidence: 99%

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Asymmetric and axisymmetric dynamics of tropical cyclones

et al. 2013

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Abstract. We present the results of idealized numerical experiments to examine the difference between tropical cyclone evolution in three-dimensional (3-D) and axisymmetric (AX) model configurations. We focus on the prototype problem for intensification, which considers the evolution of an initially unsaturated AX vortex in gradient-wind balance on an f plane. Consistent with findings of previous work, the mature intensity in the 3-D model is reduced relative to that in the AX model. In contrast with previous interpretations invoking barotropic instability and related horizontal mixing processes as a mechanism detrimental to the spin-up process, the results indicate that 3-D eddy processes associated with vortical plume structures can assist the intensification process by contributing to a radial contraction of the maximum tangential velocity and to a vertical extension of tangential winds through the depth of the troposphere. These plumes contribute significantly also to the azimuthally averaged heating rate and the corresponding azimuthal-mean overturning circulation.The comparisons show that the resolved 3-D eddy momentum fluxes above the boundary layer exhibit counter-gradient characteristics during a key spin-up period, and more generally are not solely diffusive. The effects of these eddies are thus not properly represented by the subgrid-scale parameterizations in the AX configuration. The resolved eddy fluxes act to support the contraction and intensification of the maximum tangential winds. The comparisons indicate fundamental differences between convective organization in the 3-D and AX configurations for meteorologically relevant forecast timescales. While the radial and vertical gradients of the system-scale angular rotation provide a hostile environment for deep convection in the 3-D model, with a corresponding tendency to strain the convective elements in the tangential direction, deep convection in the AX model does not suffer this tendency. Also, since during the 3-D intensification process the convection has not yet organized into annular rings, the azimuthally averaged heating rate and radial gradient thereof is considerably less than that in the AX model. This lack of organization results broadly in a slower intensification rate in the 3-D model and leads ultimately to a weaker mature vortex after 12 days of model integration. While azimuthal mean heating rates in the 3-D model are weaker than those in the AX model, local heating rates in the 3-D model exceed those in the AX model and at times the vortex in the 3-D model intensifies more rapidly than AX. Analyses of the 3-D model output do not support a recent hypothesis concerning the key role of small-scale vertical mixing processes in the upper-tropospheric outflow in controlling the intensification process.In the 3-D model, surface drag plays a particularly important role in the intensification process for the prototype intensification problem on meteorologically relevant timescales by helping foster the organization of convection in azimu...

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Section: Discussion Of Eddy Dynamicsmentioning

confidence: 99%

“…This is the "non-acceleration theorem" for inviscid, axisymmetric balance vortex dynamics (cf. McWilliams et al, 2003).…”

Section: Deductions From the Spin-up Functionmentioning

confidence: 99%

Section: Role Of Vortical Deep Convection In Tropical Cyclonesmentioning

confidence: 99%

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Asymmetric and axisymmetric dynamics of tropical cyclones

et al. 2013

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“…The sheared route of tilt decay is analogous to the familiar Thomson/Orr decay mechanism for sheared disturbances (Thomson 1887;Orr 1907;Montgomery and Kallenbach 1997;McWilliams et al 2003). The resonant-damping route of tilt decay (Briggs et al 1970) can be demonstrated analytically for the particular case of a Rankine-with-skirt vortex ( Fig.…”

Section: B Review Of Vortex Resiliency Theorymentioning

confidence: 99%

Reexamining the Near-Core Radial Structure of the Tropical Cyclone Primary Circulation: Implications for Vortex Resiliency

Mallen

Montgomery

Wang

2005

Journal of the Atmospheric Sciences

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164

142

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Recent theoretical studies, based on vortex Rossby wave (VRW) dynamics, have established the importance of the radial structure of the primary circulation in the response of tropical cyclone (TC)-like vortices to ambient vertical wind shear. Linear VRW theory suggests, in particular, that the degree of broadness of the primary circulation in the near-core region beyond the radius of maximum wind strongly influences whether a tilted TC vortex will realign and resist vertical shear or tilt over and shear apart. Fully nonlinear numerical simulations have verified that the vortex resiliency is indeed sensitive to the initial radial structure of the idealized vortex. This raises the question of how well the "true" nature of a TC's primary circulation is represented by idealized vortices that are commonly used in some theoretical studies.In this paper the swirling wind structure of TCs is reexamined by utilizing flight-level observations collected from Atlantic and eastern Pacific storms during 1977-2001. Hundreds of radial profiles of azimuthal-mean tangential wind and relative vorticity are constructed from over 5000 radial flight leg segments and compared with some standard idealized vortex profiles. This analysis reaffirms that real TC structure in the near-core region is characterized by relatively slow tangential wind decay in conjunction with a skirt of significant cyclonic relative vorticity possessing a negative radial gradient. This broadness of the primary circulation is conspicuously absent in some idealized vortices used in theoretical studies of TC evolution in vertical shear. The relationship of the current findings to the problem of TC resiliency is discussed.

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“…A TC is a natural laboratory for vortex Rossby waves. TCs are small enough that the change in Coriolis parameter f across their diameter is small, but their significant primary circulation can provide a sufficient vorticity gradient to sustain vortex Rossby waves (Montgomery and Kallenbach 1997;Möller and Montgomery 1999;McWilliams et al 2003) and potentially beta drift.…”

Section: Beta Drift On Earth and Giant Planetsmentioning

confidence: 99%

Weak Jets and Strong Cyclones: Shallow-Water Modeling of Giant Planet Polar Caps

O’Neill

Emanuel

Flierl

2016

Journal of the Atmospheric Sciences

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Giant planet tropospheres lack a solid, frictional bottom boundary. The troposphere instead smoothly transitions to a denser fluid interior below. However, Saturn exhibits a hot, symmetric cyclone centered directly on each pole, bearing many similarities to terrestrial hurricanes. Transient cyclonic features are observed at Neptune's South Pole as well. The wind-induced surface heat exchange mechanism for tropical cyclones on Earth requires energy flux from a surface, so another mechanism must be responsible for the polar accumulation of cyclonic vorticity on giant planets. Here it is argued that the vortical hot tower mechanism, claimed by Montgomery et al. and others to be essential for tropical cyclone formation, is the key ingredient responsible for Saturn's polar vortices. A 2.5-layer polar shallow-water model, introduced by O'Neill et al., is employed and described in detail. The authors first explore freely evolving behavior and then forceddissipative behavior. It is demonstrated that local, intense vertical mass fluxes, representing baroclinic moist convective thunderstorms, can become vertically aligned and accumulate cyclonic vorticity at the pole. A scaling is found for the energy density of the model as a function of control parameters. Here it is shown that, for a fixed planetary radius and deformation radius, total energy density is the primary predictor of whether a strong polar vortex forms. Further, multiple very weak jets are formed in simulations that are not conducive to polar cyclones.

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A Formal Theory for Vortex Rossby Waves and Vortex Evolution

Cited by 63 publications

References 49 publications

Asymmetric and axisymmetric dynamics of tropical cyclones

Asymmetric and axisymmetric dynamics of tropical cyclones

Reexamining the Near-Core Radial Structure of the Tropical Cyclone Primary Circulation: Implications for Vortex Resiliency

Weak Jets and Strong Cyclones: Shallow-Water Modeling of Giant Planet Polar Caps

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